Supernova from the smashing collision of a binary star

Transcription

1 Supernova from the smashing collision of a binary star Yongfeng Yang Bureau of Water Resources of Shandong Province, Jinan, Shandong Province, China, Mailing address: Shandong Water Resources Department, No. 127 Lishan Road, Jinan, Shandong Province, China, Tel. and fax: roufengyang@gmail.com Abstract Supernovae are generally believed to be triggered either in the core collapse of a massive star or in the increase of mass that a white dwarf star accumulates from a stellar companion (through accretion or merger), but a long-standing puzzle surrounding Type II supernovae is why the compact object remnant after the explosion gains a large velocity away from the core. Another unresolved problem of supernova is how to determine high rotating neutron stars that are ascribed to be a skillful kick from asymmetric collapse of a massive star, but the mechanism of this asymmetry is still unknown. Here we propose that due to orbital shrinkage the two stars of a binary star system may finally take place a smashing collision to form a supernova. The simulation of white dwarfs RX J in principle fits to the observed features of supernova. Key words: Supernova, asymmetry, binary star system, neutron star Supernova is often a kind of extremely luminous and powerful stellar explosion. Generally, supernovae are believed to be triggered either in the core collapse of a massive star [1, 2] or in the increase of mass that a white dwarf star accumulates from a stellar companion (through accretion or merger) [3]. A long-standing puzzle surrounding Type II supernovae, however, is why the compact object remnant after

2 the explosion gains a large velocity away from the core, which is generally ascribed to an asymmetry in the explosion. Neutron stars are believed to be by-products during a Type II, Type Ib or Type Ic supernova event, and they are known to have high rotation speed. Fryer ascribed this high rotation to be a skillful kick from asymmetric collapse of a massive star [4]. The initial asymmetry also occurs in Type Ia supernova explosion like SN 2001el [5]. The asymmetry (not spherically symmetric) in some cases is evident (Fig.1). Convection in the collapsing star [6] was once proposed to be responsible for this asymmetry, but later simulation showed it cannot arise in the observed results [4]. Figure 1: Asymmetric Eta Carinae. Courtesy by Jon Morse (University of Colorado) and NASA. Wang et al. thought that jet production from the neutron star may create the supernova and explain the asymmetric aftermath [5], but what causes the jets themselves to form also remains unclear. Pakmor et al in 2010 simulated a Sub-luminous type Ia supernovae through a merger of two equal-mass white dwarfs [7], but the results are also not what anyone expected [8]. Many other models [9-11] had also been tried, but still did not conform to expectation. Various suspicions suggest the established stories of the formation of supernova are incomplete. Recently Yang proposed that all objects in the universe are organized in an orderly series of

3 hierarchical two-body systems with gravitation, and expected that under the effect of gravitation the two components of a two-body the two components of each two-body system will finally collide together [12]. By this expectation, stars will collide with their planets to form novae, the two stars of a binary star system will collide each other to form a supernova. In this present paper, we theoretically run a dynamic collision of a binary star system to demonstrate the formation of a supernova. A pair of sample stars-white dwarfs RX J are here employed to carry out the simulation. RX J is an X-ray binary star system, and it is comprised of two dense white dwarf stars orbiting each other once every seconds, at an estimated distance of only miles. The stars are estimated to be about half as massive as our own sun, but only the size of the earth [13, 14]. The two stars are thought to eventually merge, based on data from the Chandra X-Ray Observatory that the orbital period of the two stars is steadily decreasing at a rate of 1.2 milliseconds per year. The components of a two-body system due to their approach will finally result in a collision. In the approach, a transformation of mechanical energy occurs that the gravitational potential energy of two components will convert to kinetic energy. Here we here consider an ideal state that there is no external factor (like resistance from other matter) to participate. First of all, we roughly estimate the transition from potential energy to kinetic energy just before a collision. The radius of each star in RX J is equal to the Earth s radius that is km, the distance between them is = km, the common center of their mass is worked out to be at a distance of km from the center of each star. To collide, each star needs to move a distance of = km towards the common center. According to a formula of gravitational potential energy, converting to kinetic energy (the formula is initially derived from an integral calculation), Where G is the gravitational constant, m 3 kg -1 s -2, M a and M b are the mass of each star, equal to 0.5 solar masses, respectively, r is the final distance of

4 each star from the common center at the moment just before the collision, L is the displacement of each star towards the common center. Thus the resulting energy for each star will be E = J. The solar mass used in the calculation is kg. The initial kinetic energy for each star at a distance of miles may be calculated through a formula, where v 0 is the initial velocity that may be calculated from orbital period and radius, namely km s-1, therefore W = J. The total energy obtained by each star will be = J. This quantity of energy may be fully converted to the kinetic energy of that star, therefore 4258 km s -1. We then allow the two stars to collide together (Fig.2). Figure 2: A successive display of the collision of the stars in a binary star system. A: Two stars are orbiting to approach each other over a long period of time; B: star a moves instantaneously along direction O 1 a 1, while star b moves along direction O 2 b 2. Both of them are approaching each other in the direction L 1 L 2. V a and V b represent their instantaneous orbital velocities respectively. Point O represents their barycenter; C: in the collision star b tangentially hits star a at position a 3, which forms a torque to spin star a; D: star a in turn hits star b at position b 3, which exerts a torque to spin star b.

5 As the two stars have high kinetic energy before a final collision, it would have to produce a strong explosion. Furthermore, because the two stars are rotationally approaching each other, the collision between them should be a tangential hit, which determines the explosion to be a non-spheroid shape. We further assumed that in the collision star a is entirely smashed while star b survives. The tangential hit may contribute a large angular momentum to star b, making it spin rapidly. Also note that the momentum obtained by star b consists of two parts. Because the two stars are moving simultaneously, when star b hits star a, a counteractive effect is produced from star a to star b, which exerts a momentum to star b, and at the same time star a also moves to hit star b, which contributes another momentum to star b, these two momenta are combined to put star b at position b 3. As the initial motions of the two stars do not lie on the same line, the tangential hit exerts a torque on O 2 b 4. Some of the two momenta can be transformed to the rotational angular momentum of star b (as shown in Figure 2(D)). We assumed the angle between the approaching direction (L 1 L 2 ) and the instantaneous motional direction of each star is the same as α (virtually it may prove that b b a a ), and then the total momentum obtained by star b at position b 3 is cos α, which is along the direction of b 3 O 2.

6 This momentum may be further divided into two parts due to the properties of geometry. One part is along direction b 3 b 4 that is used to exert a torque on b 1 O 2 to spin star b. Another part is along the direction b 3 b 5, which is used to combine with the initial momentum to determine the final motion of star b. The momentum that is used to spin star b is cosα cos α,. The length of O 2 b 4 is sin α, according to a rotational angular momentum formula for a solid homogeneous sphere 4 /5 (where is the mass of a solid sphere, r is the radius, p is the rotation period), therefore there will be an equation cosα cos α sinα 4π /5, due to,, and we further assumed α to be 45 degrees, and then p is calculated to be s, which corresponds to a orbital velocity of km s -1 for star b. At the same time, another momentum that is used to combine with the initial momentum to determine the final motion of star b is sinα cos α. The compositive velocity will be sinα cosα km s, and the direction is along O 2 b 6. This velocity determines the final motion of star b in space. Because the momentum of two stars in the collision are conservative, therefore star a earns two parts of momentum at position a 3 that is equal to cos α. According to the assumption that star a is smashed by star b, then all the momentum may be utilized to serve the motion of the remnant of star a, and the final motion is along direction O 1 a 6 (as shown in Figure 2(C)). The velocity of this motion according to a trigonometric function is cosα 2 cosα cosα 4258 km s. An ideal expectation is that star a is fully smashed in the collision, while some outer layers of star b are ripped off from the core, which may thus leave a small bulk of spheroid material to spin, thereby yielding a neutron star. Observation shows that the shape of a supernova is asymmetrical and the star remnant after the explosion gains a large velocity. Neutron stars have extremely high rotational speed and their orbital periods are between about 1.4 ms to 30 seconds. The simulation above fits to the characteristics of a supernova. In practice, the mass of two

7 stars are different, and their compactions are also different. In particular, every star holds a large quantity of thermonuclear energy in its body. The collision of two stars, which is an external effect, may induce these inner energies to instantaneously release and yield an extraordinary explosive scenario. As the two stars are approximately parallel to approach each other and result in a collision, this would determine that the momentum in the collision is transferred mainly along a plane that is parallel to the initial motional direction, thereby enabling most of the remnants of the explosion follow this plane in travel. Two spheroid-shaped shocks may thus be formed and can be observed in the illumination of later supernovae (Fig.3). For multiple star systems, the nearest two stars will at first collide with each other to form a supernova and eject spheroid-shaped shocks to spread, and subsequently the supernova and third star collide to form a new supernova and eject new spheroid-shaped shocks. It is possible that multiple spheroid-shaped shocks can be observed in multiple star systems. The established paradigm (core collapse and accretion or merger model) is unable to ride over several obstacles. Theoretically speaking, if a star relies on its own mass to collapse and explode, it is very difficult to form a powerful supernova. Because a star are composed of small units, and small units in the star s body compress each other, if a core collapse takes place, a compression between these small units increases automatically. This can arouse an outward pressure to counteract the following collapse. Furthermore, if the outward pressure still cannot counteract inward pressure and gravity, a second collapse may take place, which can further compresses the star s body. During a series of repeated collapses, a very compact star may be created. Apparently, it is impossible for a compact star to explode independently, only if some special event triggers it. In fact, since the 1960s, the core collapse is thought to be the source of the energy of a supernova explosion [1], but this is a theoretical expectation rather than an observed result. On the other hand, it is very difficult for both core collapse and accretion or merger models to account for why the compact object remnant after the explosion gains a large velocity away from the core as well the high rotation of neutron star. In addition to this, the accretion or merger model generally assumes that, before exploding in a type Ia supernova, white

8 dwarfs could not exceed the Chandrasekhar limit of a mass of about 1.4 times that of the Sun. But recent observation by Scalzo et al has provided conclusive evidence that the star itself appears to have had a mass of 2.1 times the mass of the Sun, evidently surpassing the Chandrasekhar limit [15]. In contrast, the model of smashing collision proposed here may reconcile many physical feature of a supernova. Figure 3: A simulation of the revolution of a supernova. Two stars are accelerating toward each other under the effect of gravitation (A); They continue to approach over a very long astronomical time (B); A final collision takes places, thereby producing a directed explosive supernova in space (C); With the passage of time, the remnant of explosion is promulgated mainly along a plane to form two ring-shaped shocks in a distant future (D). Reference [1] Hoyle, F., Fowler, W. A.: ApJ, 132, 565 (1960). [2] Kotake, K., Sato, K., Takahashi, K.: Rep. Prog. Phys. 69, 971(2006). [3] Mazzali, P. A., et al.: Science, 315, 825(2007). [4] Fryer, C. L.: ApJ, 601, L175 (2004).

9 [5] Wang, L. F., et al., ApJ, 591, 1110 (2003). [6] Burrows, A., Hayes, J., Phys. Rev. Lett, 76, 352(1996). [7] Pakmor, R., et al., Nature, 463, 61(2010). [8] Howell, A., Nature, 463, 35(2010). [9] Rampp, M., Janka, H-Th.: ApJL. 539, L33 (2000). [10] Thompson, T. A., Burrows, A., Pinto, P. A.: ApJ, 592, 434 (2003). [11] Sumiyoshi, K., et al.: ApJ, 629, 922 (2005). [12] Yang, Y. Y., Proceedings of the 18 th annual conference of the NPA, College Park, Maryland University, Vol.8: (2011). [13] Israel, G. L., et al.: A&A, 386: L13 (2002). [14] Antona, F. D., Ventura, P., Burderi, L., Teodorescu, A.: ApJ, 653, 1429 (2006). [15] Scalzo, R. A., et al.: ApJ, 713, 1073 (2010).